The population at the beginning of day 6 is 9720
Step-by-step explanation:
The population of bacteria triples each day; if we call
the population at the beginning of day 1, this means that the population at the beginning of day 2 is
![p_2 = 3 p_1](https://tex.z-dn.net/?f=p_2%20%3D%203%20p_1)
At the beginning of day 3,
![p_3 = 3p_2 = 3(3p_1)=9p_1](https://tex.z-dn.net/?f=p_3%20%3D%203p_2%20%3D%203%283p_1%29%3D9p_1)
At the beginning of day 4,
![p_4 = 3p_3 = 3(9p_1)=27p_1](https://tex.z-dn.net/?f=p_4%20%3D%203p_3%20%3D%203%289p_1%29%3D27p_1)
So the generic population at the beginning of day n can be written as
![p_n = 3^{t-1}p_1](https://tex.z-dn.net/?f=p_n%20%3D%203%5E%7Bt-1%7Dp_1)
where
is the population at the beginning of day 1
Therefore, by substituting t = 6, we find the population at the beginning of day 6:
![p_6 = 3^{6-1} p_1 = 243p_1 = 243(40)=9720](https://tex.z-dn.net/?f=p_6%20%3D%203%5E%7B6-1%7D%20p_1%20%3D%20243p_1%20%3D%20243%2840%29%3D9720)
Learn more about population growth:
brainly.com/question/10689103
#LearnwithBrainly
Answer:
1
(
π
3
)
)
Step-by-step explanation:
Explanation:
Substitute
tan
(
y
x
)
for
θ
tan
(
y
x
)
=
π
3
Obtain
y
x
on the left by using the inverse tangent on both sides:
tan
−
1
(
tan
(
y
x
)
)
=
tan
−
1
(
π
3
)
y
x
=
tan
−
1
(
π
3
)
Multiply both sides by x:
y
=
(
tan
−
1
(
π
3
)
)
x
Answer:
1.324
Step-by-step explanation: